The confusion between T-stops and f-stops

f-stop – we all know what that is, right? The size of the hole in the lens that lets light through. The faster the better, and the faster the more expensive. The faster it is, the easier it is to shoot in low light. An f0.95 Leica Noctilux is easily ten times more expensive than an f2.5 Leica Summarit, yet it’s only three stops faster.

That’s all. Right?

Not quite.

Zeiss ZF.2 2/28 Distagon. Notice how the front few elements almost disappear – that’s because they’re not reflecting anything. This despite a huge diffuse light source – it’s the mark of excellent coatings, and promises a T-stop close to the f-stop.

f-stop is the relationship between the physical aperture of the lens – the effective optical diameter, usually limited by the diaphragm – and the focal length. Specifically, focal length over physical aperture equals f-stop. So a 50mm f2.0 will have an effective physical aperture of 25mm. This affects one property, and one property only of the lens: the minimum depth of field. All f1.4 lenses of a given focal length will have the same depth of field. However, they may appear to have different depths of field because the speed of transition between in focus and out of focus differs depending on the optical formula of the lens. As does the quality of the bokeh. (See my other article ‘A word (or ten) on bokeh’ for more information).

The legendary Leica Noctilux.

T-stop (curiously, always written with a capital T) is a number measuring the effective transmission aperture of the lens – in other words, the physical aperture might be f2.0, but how well does the light actually transfer light to the image plane? Why would it even differ from the f-stop in the first place? Lenses are actually black holes: they absorb or reflect or refract light in directions other than the imaging plane. It could be due to poor coatings, or internal polished elements, or simply having many elements – at every air/glass or glass/glass interface, 100% transmission is impossible. There will always be some reflections which decrease the effective transmission factor of a lens.

The famous Zeiss T* coating.

Modern coatings go a very long way towards ensuring that all light entering the lens makes it to the image plane, with flare reduction and increased contrast as a bonus. However, as lens design gets more complex – take those 18-270mm super zooms for instance – the number of elements required to correct aberrations across all focal lengths covered increases, and so does the complexity of the lens design. Remember, more surfaces means less light transmission.

Leica 21/1.4 Summilux-M ASPH. Again, note how the front few elements disappear thanks to the coating. Interestingly, this is a very complex design for a Leica lens – 10 elements in 8 groups.

Practically, this means that prime lenses will generally give you a higher shutter speed for a set aperture; it might be a small difference, or a noticeable one. Your f5.6 super zooms probably have a T-stop closer to f8 or f10. Conversely, a good prime lens with few elements and excellent coatings will give a T-stop very close to the actual f-stop.

Example 1: the older Nikon 85/1.4 D has a T stop closer to T-2; the Zeiss ZF 85/1.4 Planar yields almost double the shutter speed for the same exposure, with all other variables constant. The T-stop is around T1.47.

Old Nikon 85/1.4 D – note visible reflections off every single element. That’s light that isn’t going to reach the sensor anymore.

Example 2: ignoring the minor difference in focal length, consider the Nikon 105/2.8 VR macro and the Leica 90/4 Elmarit-M macro. The Leica has only four elements. The Nikon, 14 elements in 12 groups. What do you think their T stops are? Unsurprisingly, not very different.

Not all lenses are made equal. And don’t think because there are fewer elements, the lens design isn’t as good. It’s very difficult to design a well-corrected lens with few elements – designs such as the Cooke Triplet and Double Gauss are pretty much as simple as they get. MT

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Thanks for the valuable info. I always have an impression that more elements means better – but in actuality more elements also reduces the amount of light. Usually most lenses manufacturer (including Nikon) don’t provide info on T-Stop. Any idea, if this info readily available?

It’s always a trade off: more elements means more ability to correct for the various distortions, but it also means more surfaces and yes, less light transmission because there’s a little bit lost in reflection at each surface. Nope, manufacturers don’t generally provide this info because you’d probably find that the f2.8 zooms are closer to T4; f1.4 primes are T1.8-2, and even the Leica Noctilux 0.95 is about T1.2 in reality. The highest transmission lenses – as far as I’ve been able to determine – are the Zeisses (f1.4 = T1.5) and Leica Cine Primes.

Ming, thanks for the in-depth explanation of T-Stops. This is very helpful in understanding why good glass can get such good results.

Have you any experience with the 70-300VR lens? I know that you have the 28-300 and seem to like it very much. I was just wondering if the 70-300 can provide as good of results. I know the 70-300 is much less expensive.

Yes, actually – I had the 70-300VR and traded it for the 28-300VR because I felt like I wasn’t losing any optical quality, but gaining a lot in the way of flexibility. So ye – they’re equivalent in the 70-300 range; strong from 70-200mm, weak at 300mm. There are of course tradeoffs.

Pro 70-300: 70-300 has a slightly higher T stop than the 28-300, and doesn’t suffer from focus breathing (i.e. at minimum focus distance, it’s still pretty darn close to 300mm – about 280mm by my measurements). The 28-300 at 0.5m MFD and 300mm setting is more like 135mm. Both reach 300mm at infinity. Price, too.

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[…] and most surprising side effect is a huge reduction in transmission (read my article on the difference between T stops and f stops for more detail). At any of the wide apertures, the 85/1.8 G transmits between 1/2 and 2/3 stop […]

[…] with decent (but still plausibly natural) saturation. Where they differ is in transmission: (see this article for the difference between T stops and f stops) it’s clear that the coatings used in the new […]

[…] Transmission The lens’ ability to capture light and transfer it to the image plane, limited only by the physical aperture/ iris of the lens. Applies to both the overall amount of light – T stop vs f stop – and the spectral transmission of the lens,i.e. which light spectra the actual types of glass allow through. See also this article on T stops and F stops […]